Revising 2008 Scion TC audio system (sub primarily)

Revising 2008 Scion TC audio system (sub primarily)

I bought a 2008 Scion TC recently and am happy with everything except for
the factory sub. To its credit it has what seems to be plenty of power for
me, but I'm annoyed about the way the box and the set were designed. It
seems like the audio engineers were primarily interested in getting the
boominess tuned at around 90-100 Hz, which is really annoying. I took some
foam and shoved it into the port so that the box is essentially a sealed
box. It helped a lot.

I took apart the box and found what appears to be a small unadjustable amp.
I considered putting a passive crossover in-line but didn't want to bother
building up one because I wasn't sure how low I wanted to tune it and I'd
need a bunch of different components and play around with them.

I'm at the point where I've picked apart the wiring harness to the factory
sub amp and found that there's a good 12V +/-, remote wire, and four signal
wires on the harness which might be the four channels or the +/- of two
channels. I'm guessing they are probably high-level outputs from the head
unit. I'm thinking about getting an aftermarket head unit with a built in
crossover to drive the stock 2-ohm 6.5" sub (paper cone).

Also, if I wanted to update the sub with a new speaker, would I need to get
a sub-specific speaker? Or would I be able to get any old good quality
component 6.5" speaker? I'm looking for clarity and accuracy, but I am by
no means an experienced audiophile. All I want is to bring the lows down
below 80Hz, mostly around the 40Hz region. I don't care for high volume or
license-plate rattling at all... I just want to extend the range of the lows
just a little bit more. I want to use the existing box because it
integrates well with the trunk area. And I don't want to spend more than
$100 or so. ;)

Phil